mlsanityData to 14 Oct 2026

Let us Build Bridges: Understanding and Extending Diffusion Generative Models

arXiv 2208.14699 ↗First posted 31 Aug 2022cs.LG cs.CVcited by 103

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion-based generative models have achieved promising results recently, but raise an array of open questions in terms of conceptual understanding, theoretical analysis, algorithm improvement and extensions to discrete, structured, non-Euclidean domains. This work tries to re-exam the overall framework, in order to gain better theoretical understandings and develop algorithmic extensions for data from arbitrary domains. By viewing diffusion models as latent variable models with unobserved diffusion trajectories and applying maximum likelihood estimation (MLE) with latent trajectories imputed from an auxiliary distribution, we show that both the model construction and the imputation of latent trajectories amount to constructing diffusion bridge processes that achieve deterministic values and constraints at end point, for which we provide a systematic study and a suit of tools. Leveraging our framework, we present 1) a first theoretical error analysis for learning diffusion generation models, and 2) a simple and unified approach to learning on data from different discrete and constrained domains. Experiments show that our methods perform superbly on generating images, semantic segments and 3D point clouds.

Key facts. Cited by 103 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 31 of its 44 references that are in the map. First posted on arXiv 31 Aug 2022.

Builds on

31 of 44 references.

Closest ancestors · 12

Same direction, newest first

  1. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
  2. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  3. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  4. 2021On Fast Sampling of Diffusion Probabilistic Models31 May
  5. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
  6. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  7. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  8. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  9. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  10. 2020Denoising Diffusion Implicit Models6 Oct
  11. 2020Denoising Diffusion Probabilistic Models19 Jun
  12. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 19

  1. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  2. 2016The Cityscapes Dataset for Semantic Urban Scene Understandingcited by 4,444
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  4. 2016Improved Techniques for Training GANscited by 2,970
  5. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,897
  6. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,626
  7. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  8. 2020Training Generative Adversarial Networks with Limited Datacited by 1,186
  9. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 735
  10. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 622
  11. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  12. 20213D Shape Generation and Completion through Point-Voxel Diffusioncited by 516
7 more
  1. 2015Importance Weighted Autoencoderscited by 456
  2. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 405
  3. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 262
  4. 2021Deep Generative Learning via Schr"odinger Bridgecited by 104
  5. 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
  6. 2021Score-Based Point Cloud Denoisingcited by 83
  7. 2013RNADE: The real-valued neural autoregressive density-estimatorcited by 66

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 7; 2023: 24; 2024: 32; 2025: 24; 2026: 16.

103 papers.

Sort:

By area:

  1. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  2. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
  3. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  4. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  5. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 737
  6. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 445
  7. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localizationcited by 235
  8. 2023UniControl: A Unified Diffusion Model for Controllable Visual Generation In the Wildcited by 200
  9. 2023Denoising Diffusion Bridge Modelscited by 178
  10. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Datacited by 174
  11. 2023Diffusion Schr"odinger Bridge Matchingcited by 153
  12. 2023The probability flow ODE is provably fastcited by 146
38 more
  1. 2024Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Controlcited by 143
  2. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 109
  3. 2022Diffusion-based Molecule Generation with Informative Prior Bridgescited by 106
  4. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 98
  5. 2023Error Bounds for Flow Matching Methodscited by 91
  6. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Modelscited by 85
  7. 2024Accelerating Convergence of Score-Based Diffusion Models, Provablycited by 76
  8. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplerscited by 74
  9. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 73
  10. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Modelscited by 65
  11. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptionscited by 63
  12. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theorycited by 63
  13. 2024Gradient Guidance for Diffusion Models: An Optimization Perspectivecited by 61
  14. 2023Learning Mixtures of Gaussians Using the DDPM Objectivecited by 57
  15. 2022Fast Point Cloud Generation with Straight Flowscited by 56
  16. 2023Graph Generation with Diffusion Mixturecited by 55
  17. 2024Feedback Efficient Online Fine-Tuning of Diffusion Modelscited by 53
  18. 2024Target Score Matchingcited by 50
  19. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptionscited by 50
  20. 2024Critical windows: non-asymptotic theory for feature emergence in diffusion modelscited by 47
  21. 2024Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Modelscited by 46
  22. 2023Information-Theoretic Diffusioncited by 44
  23. 2024Learning general Gaussian mixtures with efficient score matchingcited by 44
  24. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Modelscited by 39
  25. 2025Low-dimensional adaptation of diffusion models: Convergence in total variationcited by 39
  26. 2025LBM: Latent Bridge Matching for Fast Image-to-Image Translationcited by 36
  27. 2024SlimFlow: Training Smaller One-Step Diffusion Models with Rectified Flowcited by 30
  28. 2024Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallelcited by 29
  29. 2024Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Samplingcited by 27
  30. 2024Provable Acceleration for Diffusion Models under Minimal Assumptionscited by 27
  31. 2024Towards a mathematical theory for consistency training in diffusion modelscited by 26
  32. 2023Toward Understanding Generative Data Augmentationcited by 25
  33. 2023Generative Modeling with Phase Stochastic Bridgescited by 25
  34. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimatescited by 25
  35. 2025Prior Does Matter: Visual Navigation via Denoising Diffusion Bridge Modelscited by 25
  36. 2025Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixturescited by 23
  37. 2022Few-shot Image Generation with Diffusion Modelscited by 21
  38. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21

50 most cited of 103 All 103 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2024Generative Diffusion Modeling: A Practical Handbook
  2. 2024Latent Abstractions in Generative Diffusion Models
  3. 2022Understanding Diffusion Models: A Unified Perspective
  4. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models
  5. 2024Input-Adaptive Generative Dynamics in Diffusion Models
  6. 2023Neural Diffusion Models
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Models
  8. 2024Efficient Diffusion Models: A Comprehensive Survey from Principles to Practices